oversampling

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> The neurons that have "axons" -- traversing relatively large distances
> compared to their bodies -- communicate via "spikes" -- propagating
> voltage waves, driven by nonlinear equations and by external pumping of
> energy along the way, i.e., no signal degradation even for the axons that
> start at the head and end at the toes of Michael Jordan. 

Imagine how much more efficient our nervous system would be if we used
soliton waves instead of simple spikes... :)

> i.e., the brain is quite a messy telecom wiring closet. This has been
> known since the turn of the century, especially by the Spanish Anatomist
> Ramon y Cahal. 

Does anyone know what network topology our brain uses? :)

j/k

> That's because you don't need a word of Calculus to understand it -- it's
> plain algebra.

Yes, but I have to go through and re-read it five times or more (EEK! I'm
oversampling!) to understand parts of it.

> Say, one bit per doubling. That is, with 2^(14)x or 16000x oversampling.

AACK! Who ever would want that?! It's better to use a dedicated 16-bit
A/D chip!

> No. We know the spectral part because you told us explicitly in your
> previous post that this was a sine and all you needed was the amplitude.

But you cannot garuntee that in a real-world exercise. Take, for
instance, an AF data acquisition system that must be able to handle
between 10Hz and 100kHz (overlapping the AF extremes of both humans and
dolphins; assume it's an experiment for human/dolphin communications).
The ONLY thing you know is that you're interestedin the frequencies
between 10Hz and 100kHz. The exact waveshapes are completely unknown.

> That is exactly the reason I was cautious by using "level-crossing" 
> instead of "zero-crossing."

So a 1-bit A/D converter still needs an n-bit D/A converter to change the
level crossings. In other words, a 1-bit A/D converter is an incremental
successive approximation A/D converter, without the approximation
register (thus, conceivably, achieving n-times faster conversion rates,
where 'n' is the number of bits in the D/A reference converter).

(Actually, you'd need two such converters, since you're ultimately
determing whether or not the signal is within known upper and lower
bounds).

That seems like an awfully lot of complicated hardware for something that
should be quite simple.

> > > temporal resolution of about a millisecond about 100 times a second. People
> > > put this at about 3--10 bits/spike. For about 10G neurons in the brain,
> > > this means about 1 Tbyte/s _processed_. 

I'm sorry I didn't catch this earlier, but how do they assume up to 10
bits per spike? Have we measured ~1000 different timing intervals between
1ms and 10ms spike periods?

Just curious.

> Units? Of what? I was using only bits as units (apart for the volume of
> the head, which is in cu. inches and the head dissipation of the head,
> which is in Watts). 

A unit, used in this context, is a physical instantiation of a class of
hardware devices. In this case, the class would be a 1-bit A/D converter.

> > (how many people on the Internet that you know, would admit to THAT?! :D )
> 
> A) would admit WHAT?

That they are willing to admit that they don't know everything... :)

It's a joke...that's why I had a smiley there! You take some things way
too seriously! :D

> B) The Internet does not contain all interesting people and/or discussion
> topics :-) 

Didn't say it did...that's why I'm also an amateur radio operator
(KC5TJA/6)... :)

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